Method and arrangement for predicting thermally-induced deformation of a substrate, and a semiconductor device

ABSTRACT

The invention provides a method for correcting thermally-induced field deformations of a lithographically exposed substrate. First, a model is provided to predict thermally-induced field deformation information of a plurality of fields of the substrate. The pre-specified exposure information used to configure an exposure of the fields is then modified based on the thermally-induced deformation information as predicted by the model. Finally a pattern is exposed onto the fields in accordance with the pre-specified exposure information as modified. The predicting of thermally-induced field deformation information by the model includes predicting of deformation effects of selected points on the substrate. It is based on a time-decaying characteristic as energy is transported across substrate; and a distance between the selected points and an edge of the substrate.

CROSS REFERENCE TO RELATED APPLICATIONS

The present invention is a divisional of U.S. patent application Ser.No. 11/546,551, filed Oct. 12, 2006, which is a continuation-in-part ofand claims priority to U.S. patent application Ser. No. 11/247,594,filed Oct. 12, 2005. The contents of both applications are incorporatedherein by reference.

FIELD

The present invention relates to an arrangement and a method formanufacturing a device and to a device.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.comprising part of, one, or several dies) on a substrate (e.g. a siliconwafer). Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned. Known lithographic apparatusinclude so-called steppers, in which each target portion is irradiatedby exposing an entire pattern onto the target portion at one time, andso-called scanners, in which each target portion is irradiated byscanning the pattern through a radiation beam in a given direction (the“scanning”-direction) while synchronously scanning the substrateparallel or anti-parallel to this direction. It is also possible totransfer the pattern from the patterning device to the substrate byimprinting the pattern onto the substrate.

The demand for smaller and smaller semiconductor devices drives the needto have lithographic fabrication processes achieve pattern features andprofiles having smaller critical dimensions. Moreover, such devices maycomprise multiple layers, requiring precise positioning of successivelayers over one or more prior layers. It is important that these smallerdevices are consistently reproduced with as little overlay errors aspossible to yield high-quality devices.

During a lithographic fabrication process, there are, however, numerousactivities that contribute to overlay errors and compromise the qualityof the exposed patterns. In particular, an exposed substrate is subjectto thermal energy. In case of an optical lithographic apparatus thethermal energy substrate heating may result in deformations of a fieldon the substrate under exposure. In an immersion lithographic apparatusthe substrate deformation is caused by immersion liquid evaporation thatinduces deformations of each field. Such thermally-induced deformationsmay result in unacceptable overlay and focusing errors and significantlyreduce yield production.

SUMMARY

It is desirable to provide a method for predicting thermally-inducedfield deformations of a substrate to be exposed lithographically with animproved performance in view of the prior art.

To that end, the invention provides a method for predictingthermally-induced field deformation of a substrate to be exposedlithographically comprising:

providing pre-specified exposure information;

using a model to predict thermally-induced field deformation at selectedpoints of the substrate based on the pre-specified exposure information;

wherein the model is based on

a time-decaying characteristic as energy is transported across saidsubstrate; and

a distance between the selected points and an edge of said substrate.

The invention further provides a semiconductor device produced withaforementioned method.

The invention further provides an arrangement for predictingthermally-induced field deformation of a substrate characterized by:

an input port arranged to received pre-specified exposure information;

a processor unit connected to the input port and arranged to employ amodel to predict thermally-induced field deformation at selected pointsof the substrate to be exposed based on the received pre-specifiedexposure information, wherein the model is based on

a time-decaying characteristic as energy is transported across saidsubstrate and to determine improved exposure information based on thepredicted thermally induced field deformation; and

a distance between the selected points and an edge of said substrate.

Finally, the invention further relates to a semiconductor deviceproduced with aforementioned arrangement.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying schematic drawings in whichcorresponding reference symbols indicate corresponding parts, and inwhich:

FIG. 1 depicts a lithographic apparatus according to an embodiment ofthe invention;

FIGS. 2 and 3 show a liquid supply system used in a prior artlithographic projection apparatus;

FIGS. 4 a and 4 b show a liquid supply system according to another priorart lithographic projection apparatus;

FIG. 5 shows a further view of the liquid supply system according to aprior art lithographic projection apparatus;

FIGS. 6 a-e illustrate various thermally-induced target fielddeformations;

FIG. 7 schematically shows an exemplary trajectory of a projectionsystem with respect to a substrate to be exposed in a prior artlithographic projection apparatus;

FIG. 8 schematically shows a schematic function flow diagram depictingan embodiment of the present invention;

FIG. 9 schematically shows a decomposition of a predictivetime-dependent deformation effect in accordance with an embodiment ofthe present invention.

FIG. 10 schematically shows a decomposition of a distance to an edge ofa substrate as employed in an embodiment of the present invention;

FIG. 11 shows an arrangement according to an embodiment of the presentinvention.

DETAILED DESCRIPTION

FIG. 1 schematically depicts a lithographic apparatus according to oneembodiment of the invention. The apparatus comprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. UV radiation or EUV-radiation).    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WT constructed to hold a        substrate (e.g. a resist-coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate in accordance with certain parameters; and    -   a projection system (e.g. a refractive projection lens system)        PS configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies) of the substrate W.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

The support structure supports, i.e. bears the weight of, the patterningdevice. It holds the patterning device in a manner that depends on theorientation of the patterning device, the design of the lithographicapparatus, and other conditions, such as for example whether or not thepatterning device is held in a vacuum environment. The support structurecan use mechanical, vacuum, electrostatic or other clamping techniquesto hold the patterning device. The support structure may be a frame or atable, for example, which may be fixed or movable as required. Thesupport structure may ensure that the patterning device is at a desiredposition, for example with respect to the projection system. Any use ofthe terms “reticle” or “mask” herein may be considered synonymous withthe more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore substrate tables (and/or two or more mask tables). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as an integrator IN and acondenser CO. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross-section.

The radiation beam B is incident on the patterning device (e.g., maskMA), which is held on the support structure (e.g., mask table MT), andis patterned by the patterning device. Having traversed the mask MA, theradiation beam B passes through the projection system PS, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g. an interferometricdevice, linear encoder or capacitive sensor), the substrate table WT canbe moved accurately, e.g. so as to position different target portions Cin the path of the radiation beam B. Similarly, the first positioner PMand another position sensor (which is not explicitly depicted in FIG. 1)can be used to accurately position the mask MA with respect to the pathof the radiation beam B, e.g. after mechanical retrieval from a masklibrary, or during a scan. In general, movement of the mask table MT maybe realized with the aid of a long-stroke module (coarse positioning)and a short-stroke module (fine positioning), which form part of thefirst positioner PM. Similarly, movement of the substrate table WT maybe realized using a long-stroke module and a short-stroke module, whichform part of the second positioner PW. In the case of a stepper (asopposed to a scanner) the mask table MT may be connected to ashort-stroke actuator only, or may be fixed. Mask MA and substrate W maybe aligned using mask alignment marks M1, M2 and substrate alignmentmarks P1, P2. Although the substrate alignment marks as illustratedoccupy dedicated target portions, they may be located in spaces betweentarget portions (these are known as scribe-lane alignment marks).Similarly, in situations in which more than one die is provided on themask MA, the mask alignment marks may be located between the dies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the mask table MT and the substrate table WT are keptessentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e. asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the mask table MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the masktable MT may be determined by the (de-)magnification and image reversalcharacteristics of the projection system PS. In scan mode, the maximumsize of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the mask table MT is kept essentially stationaryholding a programmable patterning device, and the substrate table WT ismoved or scanned while a pattern imparted to the radiation beam isprojected onto a target portion C. In this mode, generally a pulsedradiation source is employed and the programmable patterning device isupdated as required after each movement of the substrate table WT or inbetween successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

Different solutions are known to provide a lithographic apparatus usingimmersion techniques. A known system for providing a liquid is to use asystem to provide liquid on only a localized area of the substrate W andin between a final element FE of the projection system PL and thesubstrate W using a liquid confinement system (substrate W generally hasa larger surface area than the final element FE of the projection systemPL). A known way to arrange for this is illustrated in FIGS. 2 and 3, inwhich liquid is supplied by at least one inlet IN onto the substrate W,preferably along the direction of movement of the substrate W relativeto the final element FE, and is removed by at least one outlet OUT afterhaving passed under the projection system PL. That is, as the substrateW is scanned beneath the element in a −X direction, liquid is suppliedat the +X side of the element and taken up at the −X side.

FIG. 2 schematically shows the arrangement in which liquid is suppliedvia inlet IN and is taken up on the other side of the element by outletOUT which is connected to a low pressure source. In FIG. 2, the liquidis supplied along the direction of movement of the substrate W relativeto the final element FE, though this does not need to be the case.Various orientations and numbers of in- and out-lets positioned aroundthe final element are possible. One example is illustrated in FIG. 3 inwhich four sets of an inlet with an outlet on either side are providedin a regular pattern around the final element.

Another solution which has been proposed is to provide the liquid supplysystem with a seal member which extends along at least a part of aboundary of the space between the final element FE of the projectionsystem PL and the substrate table WT. Such a solution is illustrated inFIG. 4. The seal member is substantially stationary relative to theprojection system in the XY plane though there may be some relativemovement in the Z direction (in the direction of the optical axis). Aseal is formed between the seal member and the surface of the substrate.Preferably the seal is a contactless seal such as a gas seal.

In an immersion arrangement, a liquid 11 is pumped into one side of theapparatus and out of the other side of the apparatus. As shown in FIG.5, a reservoir 10 forms a contactless seal to the substrate W around animage field of the projection system PL so that liquid is confined tofill a space between the substrate surface and the projection system PL,and in one embodiment between the substrate W and the final element FEof the projection system PL. The reservoir 10 is formed by a seal member12 positioned below and surrounding the final element FE of theprojection system PL. Liquid 11 is brought into the space below theprojection system PL and within the seal member 12. The seal member 12extends a little above a lower surface of the final element FE of theprojection system and the liquid level rises above the final element FEsuch that a buffer of liquid is 11 provided. The liquid filled space ofseal member 12 has an inner periphery that at the upper end preferablyclosely conforms to the shape of the projection system PL or the finalelement FE thereof and may, e.g., be round. At the bottom, the innerperiphery of the liquid filled space closely conforms to the shape ofthe image field, e.g., rectangular though this need not be the case.

The liquid 11 is confined in the reservoir 10 by a gas seal 16 betweenthe bottom of the seal member 12 and the surface of the substrate W. Thegas seal 16 is formed by gas, e.g. air or synthetic air but preferablyN₂ or another inert gas, provided under pressure via an inlet 15 to thegap between seal member 12 and substrate W and extracted via a firstoutlet 14. An overpressure on the gas inlet 15, a lower pressure (e.g. avacuum level) on the first outlet 14 and geometry of the gap arearranged such that there is a high-velocity air flow inwards thatconfines the liquid 11.

A lithographic exposure process employed to project a pattern on targetfield C on substrate W may cause pattern deformations, like patternshifts, due to absorption or dissipation of thermal energy by thesubstrate W during exposure. Such thermally induced deformations mayresult in unacceptable overlay errors in the substrate W. In anon-immersion lithographic exposure apparatus, these thermally-induceddeformations do result from an absorption of thermal energy, which heatsup the substrate W locally. In an immersions system, however, thesethermally-induced deformations result from cooling of the substrate Wdue to evaporation of the immersion liquid 11.

Target field deformations may occur in different forms. They includetranslation deformations (FIG. 6 a), magnification deformations (FIG. 6b), rotational deformations (FIG. 6 c), shape deformations (FIG. 6 d)and/or any combination thereof (FIG. 6 e).

FIG. 7 schematically shows an exemplary trajectory of reservoir 10present underneath a projection system PL over a substrate W in a priorart lithographic projection apparatus during exposure. The substrate Wcomprises a number of target fields C_(i) (i=1, . . . , N). Throughoutthis description, target field C_(i) is presented as an area with acertain size and positioned at a certain location on substrate W.However, it must be understood that target field C_(i) may also refer toan area on a different substrate than substrate W, e.g. to any targetarea on a subsequent substrate within a batch, the target area having asimilar size and present at a similar location as C_(i) would have onsubstrate W.

The way in which a target field C_(i) is affected, depends among otherson the thermal properties of the substrate W, such as absorption,conduction, radiation etc. and similar thermal properties of patternsthat are positioned on the substrate W during earlier exposures.

An exposure of target field C_(i) may also heat adjacent target fieldsC_(i+k) surrounding target field C_(i). As the successive adjacenttarget field C_(i+1) is subsequently exposed, the preceding target fieldC_(i) proceeds to cool, but may also experience some residual heatingdue to the exposure of target field C_(i+1). Consequently, size, numberand mutual spacing of the target fields C_(i) on the substrate W areimportant parameters that have an influence on overlay errors due tothermal deformations by heating.

Moreover, in an immersion lithographic apparatus, while exposing targetfield C_(i), the substrate W may be cooled down by water evaporationcausing all consecutive fields C₁-C_(N) to be deformed. Although size,number and spacing of the target fields C_(i) also play a role inthermal deformation by cooling, more important for a cooling process isthe exposure sequencing. For example, introducing different field sizemay lead to a situation wherein the sequencing of exposure is changed.This change introduces another thermal deformation effect. However,different field size does not have to lead to a different deformationpattern if the path followed by the substrate is not changed. Note thatthis is different for substrate heating by exposure, since in that casefield size plays an important role due to the fact that a substratereceives a different amount of energy.

FIG. 8 schematically depicts a flow diagram of the general inventiveconcept of thermal correction process 100, constructed and operative inaccordance with a particular embodiment of the present invention. Thecorrection process starts with two actions, i.e. action 102 and action104.

In action 102 an initial exposure recipe is provided. The exposurerecipe designates an amount of energy to be focused by the projectionbeam PB onto each target field C₁-C_(N) of substrate W to comply withfeatures that are specified by a manufacturer and profile of the exposedpattern. The exposure recipe may include exposure time, exposure energy,exposure coordinate positioning and exposure sequencing.

In action 104, a model is provided to predict thermally-induced fielddeformation information of a plurality of fields on a substrate. Themodel may use the pre-specified exposure information, as provided inaction 102. The prediction of the thermally-induced deformationinformation may be modeled as:

${\Delta\; r} \approx {\sum\limits_{i}{T_{i}D_{i}}}$where

Δr represents the predictive time-dependent deformation effects;

T_(i), represents timing effects in a point i; and

D_(i) represents spatial effects of a point i.

As shown in FIG. 9, Δr may be expressed as a function of dx_(p) anddy_(p), i.e. Δr=(dx_(p),dy_(p)), where x_(p) and y_(p) are predictivetime-dependent deformation effects in an x and y-direction respectively.

Thus the following set of calculated predictive temporal deformationinformation may be calculated as follows:

${dx}_{p} = {\sum\limits_{i}{T_{i}^{x}D_{i}^{x}}}$

${dy}_{p} = {\sum\limits_{i}{T_{i}^{y}D_{i}^{y}\mspace{14mu}{where}}}$

T_(i) ^(x) represents timing effects of exposing a target field C_(i) inan x-direction;

T_(i) ^(y) represents timing effects of exposing a target field C_(i) ina y-direction;

D_(i) ^(x) represents spatial effects in the x-direction induced by adistance between a point within an exposed target field C_(i) and apoint in a target field to be currently exposed;

D_(i) ^(y) represents spatial effects in the y-direction induced by adistance between a point within an exposed target field C_(i) and apoint in a target field to be currently exposed.

a. Exposure Heating

In this case, the prediction of the thermally-induced deformationinformation is significantly affected by local deformations that arecaused by the energy applied on previously-exposed dies. Therefore, incase of deformations induced by heating of a target field C_(i), i.e. adie, as a result of a lithographic exposure, T_(i) and D_(i) may beexpressed as:

$T_{i} = {\exp( {- \frac{t - t_{i}}{\tau}} )}$where τ represents a time sensitivity constant which depends on thethermal properties of the lithographic exposure components;

t represents absolute time; and

t_(i) represents time during which target field C_(i) is exposed.

and

$D_{i} = {k\mspace{14mu}{\exp( {- \frac{{r_{i} - r}}{\chi}} )}\mspace{14mu}{where}}$

r_(i) represents a point on target field C_(i) at which overlay isestimated, the point lying on the exposure route that is followed byreservoir 10 filled with liquid 11;

r represents a point on the substrate W that is currently being exposed;

χ represents spatial thermal properties of the lithographic exposurecomponents (e.g. exposure chuck, substrate processing, etc.), and

k represents a proportionality constant that depends on thermalproperties of the lithographic exposure components but will generally beconstant for a given set of components.

The thermal effects of exposing a target field C_(i) will decay in timeas energy is transported across the substrate W. The spatial effectsrelate to the distance |r_(i)−r| between an exposed target field C_(i)and a target field to be exposed.

b. Immersion Cooling

In this case, the prediction of the thermally-induced deformationinformation is significantly affected by the energy applied on asubstrate W while exposing previous dies. Consequently, the thermaleffects T_(i) are modeled in a similar way as for exposure heating.However, the spatial effects are modeled in a different way. Incomparison to exposure heating, thermal deformation is not limited tothe field C_(i) that is exposed during a certain period of time. Liquid11 covers a larger area, and evaporation of the liquid 11 may well occuraway from the field, e.g. at the circumference of reservoir 10. Thermaldeformation on a point r ₀ caused by this cooling phenomenon may now beestimated by:

${\overset{\_}{F}( {{\overset{\_}{r}}_{0},{\overset{\_}{r}}_{c}} )} = {\sum\limits_{{i\text{:}{\overset{\_}{r}}_{i}} \in {{{SH}{({\overset{\_}{r}}_{c})}}\bigcap W}}^{N}{( {{\overset{\_}{r}}_{i} - {\overset{\_}{r}}_{0}} ){{\exp( {{- {{{\overset{\_}{r}}_{i} - {\overset{\_}{r}}_{0}}}}/\chi} )}/{{{\overset{\_}{r}}_{i} - {\overset{\_}{r}}_{0}}}}\mspace{14mu}{where}}}$

r ₀ represents a point where overlay is estimated;

SH( r) represents a combination of final element FE of the projectionsystem PL, reservoir 10, liquid 11 and seal member 12, also referred toas “showerhead” SH;

r _(c) represents a position of a center of the showerhead SH duringexposure of a substrate; and

N is a maximal number needed for integral estimation.

During exposure of a substrate W, shower head SH follows a substrateexposure route, i.e. as shown in FIG. 7.

As a result an overlay effect on the substrate W may be estimated by:

$\begin{matrix}{{d\;{\overset{\_}{r}( {\overset{\_}{r}}_{j} )}} = {\sum\limits_{i = 0}^{j}{{\overset{\_}{F}( {{\overset{\_}{r}}_{j},{\overset{\_}{r}}_{i}} )}T_{ij}}}} \\{= {\sum\limits_{i = 0}^{j}{{\overset{\_}{F}( {{\overset{\_}{r}}_{j},{\overset{\_}{r}}_{i}} )}{\exp( {{- {{t_{i} - t_{j}}}}/\tau} )}}}}\end{matrix}$

Now, D_(i) may be rewritten as:

${D( {{\overset{\_}{r}}_{i},\overset{\_}{r}} )} = {\sum\limits_{{i\text{:}{\overset{\_}{r}}_{j}} \in {{{SH}{({\overset{\_}{r}}_{c})}}\bigcap W}}^{N}{( {{\overset{\_}{r}}_{j} - {\overset{\_}{r}}_{i}} ){{\exp( {{- {{{\overset{\_}{r}}_{j} - {\overset{\_}{r}}_{i}}}}/\chi} )}/{{{\overset{\_}{r}}_{j} - {\overset{\_}{r}}_{i}}}}\mspace{14mu}{where}}}$

r_(i) represents a point on target field C_(i);

r represents a point on the substrate W that is currently being followedby the showerhead SH;

χ: represents spatial thermal properties of lithographic exposurecomponents;

N is a maximal number needed for integral estimation; and

W is the substrate.

D_(i) is thus calculated for each pair of points as a summation of thethermal effects on the substrate taken along the radius of theshowerhead with its center in one point and with respect to anotherpoint.

Aforementioned thermal analysis, however, does not take into account anyadditional thermally-induced deformations caused by edge effects on thesubstrate W. On an edge, the substrate W has less constraints to deform,and therefore thermally-induced deformations have a different nature atsuch a location.

Therefore, in an embodiment of the present invention, in addition toaforementioned thermal disturbances of adjacent dies within thesubstrate, within the model also an edge effect is estimated. Thisestimate may be calculated by including one or more of the following:

1. A deformation on an edge of a substrate depends on a distance of anenergy source from the edge of the substrate. To estimate an edge effectthe minimum distance from a point to the edge may be taken into account.

The distance to the edge, schematically shown in FIG. 10, is calculatedasx ^(e)( r _(i))=min(|x _(i)−√{square root over (R ² −y _(i) ²)}|,|x_(i)+√{square root over (R ² −y _(i) ²)}|)y ^(e)( r _(i))=min(|y _(i)−√{square root over (R ² −x ₁ ²)}|,|y_(i)+√{square root over (R ² −x _(i) ²)}|) where

x^(e) represents a distance to an edge of substrate W in an x-direction;

y^(e) represents a distance to an edge of substrate W in a y-direction;

x_(i) represents an x-coordinate of r₁;

y_(i) represents an y-coordinate of r_(i); and

R represents a radius of substrate W.

An edge overlay effect would then be estimated as:

${d\;{\overset{\sim}{x}( {\overset{\_}{r}}_{i} )}} = {\frac{d\;{\overset{\_}{r}( {\overset{\_}{r}}_{i} )}_{x}}{{d\;{\overset{\_}{r}( {\overset{\_}{r}}_{i} )}}}/( {p_{1}^{x} + {p_{2}^{x}x_{i}^{e}}} )}$${d\;{\overset{\sim}{y}( {\overset{\_}{r}}_{i} )}} = {\frac{d\;{\overset{\_}{r}( {\overset{\_}{r}}_{i} )}_{y}}{{d\;{\overset{\_}{r}( {\overset{\_}{r}}_{i} )}}}/( {p_{1}^{y} + {p_{2}^{y}y_{i}^{e}}} )}$where

d{tilde over (x)}( r _(i)) and d{tilde over (y)}( r _(i)) are firstestimates of an edge overlay effect in an x-direction and y-directionrespectively;

d r( r _(i))_(x) is a deformation that is caused by the projectionsystem PL with immersion liquid 11 at point r _(i) of which d r( r_(i))_(x) and d r( r _(i))_(y) are x and y components respectively; and

p_(1,2) ^(x,y) are first and second parameters respectively in x- andy-direction respectively that are obtained by a fit.

2. In the case of immersion cooling, edge deformations also depend on anamount of energy that is transferred from the substrate W to theimmersion liquid 11 between the substrate W and the projection systemPL. It can be estimated that this dependency can be taken to beproportional to a logarithm of the period during which the immersionliquid remains on the substrate W. In the model it may be realized as:

${{dx}_{edge}( {\overset{\_}{r}}_{i} )} = {{\log( {f_{i} + 1} )}\frac{d\;{\overset{\sim}{x}( {\overset{\_}{r}}_{i} )}}{\log(M)}}$${{dy}_{edge}( {\overset{\_}{r}}_{i} )} = {{\log( {f_{i} + 1} )}\frac{d\;{\overset{\sim}{y}( {\overset{\_}{r}}_{i} )}}{\log(M)}\mspace{14mu}{where}}$

dx_(edge)( r _(i)) and dy_(edge)( r _(i)) represent further estimates ofan edge overlay effect in the x- and y-direction respectively in whichthe dependency upon the amount of energy taken by liquid 11 in reservoir10 is taken into account.

f_(i) represents an index of a point that is being exposed according toa route of exposure; and

M represents a total number of points.

It can be seen that dx_(edge)( r _(i)) and dy_(edge)( r _(i)) willlargely grow when r _(i) would come closer to the edge of the substrateW. To avoid this, a minimum edge distance correction can be introduced,which may take the form of:Y( r _(i))=max(| r _(i)|,0.95·R) where

Y( r _(i)) represents the minimum edge distance correction.

With this correction, the distance to an edge of substrate W in thex-direction and y-direction respectively, may be expressed as:

${x^{e}( {\overset{\_}{r}}_{i} )} = {\min\begin{pmatrix}{{{{x_{i}/{Y( {\overset{\_}{r}}_{i} )}} - \sqrt{R^{2} - {y_{i}^{2}/{Y^{2}( {\overset{\_}{r}}_{i} )}}}}},} \\{{{x_{i}/{Y( {\overset{\_}{r}}_{i} )}} + \sqrt{R^{2} - {y_{i}^{2}/{Y^{2}( {\overset{\_}{r}}_{i} )}}}}}\end{pmatrix}}$ and${y^{e}( {\overset{\_}{r}}_{i} )} = {\min\begin{pmatrix}{{{{y_{i}/{Y( {\overset{\_}{r}}_{i} )}} - \sqrt{R^{2} - {x_{i}^{2}/{Y^{2}( {\overset{\_}{r}}_{i} )}}}}},} \\{{{y_{i}/{Y( {\overset{\_}{r}}_{i} )}} + \sqrt{R^{2} - {x_{i}^{2}/{Y^{2}( {\overset{\_}{r}}_{i} )}}}}}\end{pmatrix}}$

A set of total overlay corrections may then be expressed as:dx _(i) ^(total) =dx( r _(i) ,C ₁ ^(x) ,C ₂ ^(x),χ^(x),τ^(x) ,p ₁ ^(x),p ₂ ^(x))=C ₁ ^(x) d r ( r _(i),χ^(x),τ^(x))_(x) +C ₂ ^(x) dx _(edge)(r _(i) ,d r ( r _(i)),p ₁ ^(x) ,p ₂ ^(x))dy _(i) ^(total) =dy( r _(i) ,C ₁ ^(y) ,C ₂ ^(y),χ^(y),τ^(y) ,p ₁ ^(y),p ₂ ^(y))=C ₁ ^(y) d r ( r _(i),χ^(x),τ^(x))_(y) +C ₂ ^(y) dx _(edge)(r _(i) ,d r ( r _(i)),p ₁ ^(y) ,p ₂ ^(y))where

dx_(i) ^(total) and dy_(i) ^(total) represent the total overlaycorrection in the x-direction and y-direction respectively at a pointr₁;

τ^(x) and τ^(y) represent a time sensitivity constant which depends onthe thermal properties of the lithographic exposure components for thex-direction and y-direction respectively;

χ^(x) and χ^(y) represent spatial thermal properties of the lithographicexposure components (e.g. exposure chuck, substrate processing, etc.) inan x-direction and y-direction respectively; and

C_(1,2) ^(x,y) are first and second constants respectively in anx-direction and y-direction respectively, of which the first constantcorresponds to the term related to an overlay correction due to a bulkeffect and the second constant corresponds with the term related to anoverlay correction due to an edge effect.

Thermal correction process 100 then advances to action 106, i.e.modifying the pre-specified exposure information based onthermally-induced deformation information as predicted by the model.Thus, by having a prediction as to how thermal effects deform a targetfield C_(i) as energy is transported across the wafer substrate W, thepredicted deformation information may be used to modify thepre-specified exposure information for each target field C₁-C_(N) inorder to reduce chances of overlay errors in a field C_(i). The modifiedpre-specified exposure information may include calculated exposureposition offsets to adjust exposure coordinate positions or otheradjustable exposure parameters.

In action 108, thermal correction process 100 continues by selectingwhether a first exposure with the pre-specified exposure information asmodified in action 106 will be exposed. It must be noted that in otherembodiments of the invention this choice may be applied more often, andwill not be limited to the first exposure. Furthermore, it must beunderstood that first exposure is not limited to the first exposure of aspecific substrate. It may also refer to a first exposure of a specificpattern to be exposed on a batch of substrates.

If it is the first exposure, thermal correction process 100 continues toaction 110, i.e. exposing fields C₁-C_(N) on substrate W withpre-specified exposure information as modified in action 106. Thus eachof the target fields C₁-C_(N) is exposed with the desired pattern via alithographic apparatus in accordance with the modified pre-specifiedexposure information, including applied dosages, exposure coordinatepositioning and exposure sequencing. It must be understood that action108 may be absent. In this case the method directly continues withexposing fields in accordance with action 110 after modification of thepre-specified exposure information in action 106.

Finally, as will be clear for a person skilled in the art, the method asdescribed thus far does not need to be applied to all substrates withina batch. After modifying the pre-specified exposure information based onthermally-induced deformation information as predicted by the model,i.e. action 106, all substrates within the batch reserved to undergo thesame exposure, may be exposed with the same pre-specified exposureinformation as modified.

It may well be that aforementioned modifications do not compensate forall thermally-induced deformations. Therefore, it is possible to enhancethermal correction process 100 further by measuring attributes of theexposed fields on the substrate W in action 112. The measuring isconfigured to measure various attributes and artifacts of target fieldsC₁-C_(N) and/or substrate W that evince thermal effects, like cooling.Such measured attributes may include, for example, size of individualtarget fields C, specific test patterns, layer dependent alignmentmarks, gaps between target field C features, X and/or Y diameter oftarget fields, holes and/or posts etc. and may be performed bymechanisms internal to lithographic exposure apparatus or by externaldevices.

Based on the measured attributes of the exposed target fields C₁-C_(N),thermal correction process 100 determines in action 114 correctiveinformation to revise the predicted thermally-induced deformationinformation. This means that the information obtained by the measurementof attributes may lead to an updated set of predictive deformations fora plurality of selected points within each target field C_(i).

The updated set of predictive deformations for a plurality of selectedpoints within each target field C_(i) as determined in action 114 may beused, in action 116, to adjust the pre-specified exposure information,which was already modified in action 106. The corrective informationoffsets are then fed back to the modified pre-specified exposureinformation for adjustment, so the modified and adjusted pre-specifiedexposure information may be used, in action 110, for subsequentexposure, e.g. on subsequent substrates in a batch.

It should be understood that, alternatively, in action 110, a singletarget field C_(i) may be exposed with pre-specified information asmodified. In action 112, the attributes of this target field C_(i) maythen be measured, and based on these attributes as measured, in action114, corrective information may be determined. The pre-specifiedexposure information as modified may then, in action 116, be adjustedbased on this corrective information. Finally, subsequent fields C_(i)on the same substrate W may be exposed with pre-specified exposureinformation as modified and adjusted in action 110, etc.

The pre-specified exposure information may include exposure time,exposure sequencing, and exposure coordinate information. Actions 110,112, 114, 116 in thermal correction process 100 may be iterated severaltimes, e.g. on subsequent substrates in a batch, until the exposedpatterns within the fields C₁-C_(N) on the substrates achieve desiredfeatures and profile specified by a manufacturer by the originalpre-specified exposure information. Subsequent substrates may then beexposed by the pre-specified exposure information as modified andadjusted in accordance with the last results of the iteration process.

The arrow between action 108 and action 116 denotes the situation forsubstrates in a batch of substrates that are reserved to undergo thesame exposure as the first substrate(s) for which corrective informationis determined on the basis of measured attributes in actions 114 and 112respectively. As the pre-specified exposure information as modified isalready adjusted based on aforementioned corrective information, thesesubstrates may be exposed directly with the latter exposure informationin action 110.

FIG. 11 depicts a lithography apparatus 201 according to an embodimentof the present invention. In this embodiment, the substrate, which isexposed with the lithographic apparatus 201, is transferred (afterdevelopment by a track) to a measurement station 202. The measurementstation 202 is connected to a processor unit 203 that includes aprocessor 204 and a memory 205. The measurement station 202 measuresattributes of a plurality of fields provided on the substrate. Themeasurement station 202 is arranged to obtain measurement data and toprovide these measurement data to the processor unit 203. In the memory205 of the processor unit 203, pre-specified exposure information may bestored regarding the pattern to be exposed on a substrate W. Theprocessor 204 of the processor unit 203 is used to determine a model topredict thermally-induced field deformation information of the pluralityof field of substrate W by comparing the measurement data, received fromthe measurement station 202, and the pre-specified exposure information,stored in the memory 205. The determined model may be stored in memory205 as well. With the determined model, the processor unit 203 iscapable of predicting thermally-induced field deformation informationand modify the pre-specified exposure information. The processor unit203 may provide the modified pre-specified exposure information to thelithographic apparatus 201. The lithographic apparatus 201 may use thisinformation in an exposure of subsequent substrates W.

In an alternative embodiment, the derived values of these parameters arenot supplied to the lithographic apparatus 201, but to a differententity, like a track, a computer terminal or a display. In the lattercase, an operator, who is responsible for the operation of thelithographic apparatus 201, may then be able to check whether predictedoverlay errors fall within preset overlay requirements or not. In yetanother embodiment, the mathematical model may be stored in a differententity than the processor unit 203. In an embodiment of the invention,both the lithographic apparatus 201 and the measurement station 202 maybe connected to the same track in order to efficiently controlparameters of the lithographic apparatus 202.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin-film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

Although specific reference may have been made above to the use ofembodiments of the invention to compensate for cooling caused byevaporation of an immersion liquid in an immersion lithographicapparatus, it must be understood that several embodiments of theinvention may also be used to compensate for thermally-induceddeformation that are caused by heating of the substrate due to radiationin a conventional optical lithographic apparatus, i.e. an opticallithographic apparatus without the presence of an immersion liquid.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g. having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

One or more embodiments of the invention may be applied to any immersionlithography apparatus, in particular, but not exclusively, those typesmentioned above and whether the immersion liquid is provided in the formof a bath or only on a localized surface area of the substrate. A liquidsupply system as contemplated herein should be broadly construed. Incertain embodiments, it may be a mechanism or combination of structuresthat provides a liquid to a space between the projection system and thesubstrate and/or substrate table. It may comprise a combination of oneor more structures, one or more liquid inlets, one or more gas inlets,one or more gas outlets, and/or one or more liquid outlets that provideliquid to the space. In an embodiment, a surface of the space may be aportion of the substrate and/or substrate table, or a surface of thespace may completely cover a surface of the substrate and/or substratetable, or the space may envelop the substrate and/or substrate table.The liquid supply system may optionally further include one or moreelements to control the position, quantity, quality, shape, flow rate orany other features of the liquid.

The immersion liquid used in the apparatus may have differentcompositions, according to the desired properties and the wavelength ofexposure radiation used. For an exposure wavelength of 193 nm, ultrapure water or water-based compositions may be used and for this reasonthe immersion liquid is sometimes referred to as water and water-relatedterms such as hydrophilic, hydrophobic, humidity, etc. may be used.

While specific embodiments of the invention have been described above,it will be appreciated that the invention may be practiced otherwisethan as described. For example, the invention may take the form of acomputer program containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g. semiconductor memory, magnetic or optical disk) having sucha computer program stored therein.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made to the invention as described without departing from thescope of the claims set out below.

1. An arrangement for predicting thermally-induced field deformation ofa substrate, comprising: an input port arranged to receivedpre-specified exposure information; a processor unit connected to theinput port and arranged to employ a model to predict thermally-inducedfield deformation at selected points of the substrate to be exposedbased on the received pre-specified exposure information, wherein themodel is based on a time-decaying characteristic as energy istransported across said substrate and to determine improved exposureinformation based on the predicted thermally induced field deformation;and a distance between the selected points and an edge of saidsubstrate.
 2. The arrangement of claim 1, wherein the arrangementcomprises a track.
 3. The arrangement of claim 1, wherein the model isfurther based on a distance between the selected points and an energysource.
 4. The arrangement of claim 1, wherein the processor is arrangedto determine enhanced exposure information based on the predictedthermally induced field deformation.
 5. The arrangement of claim 4,wherein the processor is arranged to determine enhanced exposureinformation by adjusting exposure field sequencing information.
 6. Thearrangement of claim 4, wherein the arrangement exposes a plurality offields using the enhanced exposure information.
 7. The arrangement ofclaim 6, wherein each field of said plurality of fields has one or moreof the selected points.
 8. The arrangement of claim 6 wherein: ameasurement port is arranged to receive measurements regardingattributes of an exposed first field of said plurality of fields; theprocessor unit is connected to the measurement port and arranged to (a)assess deformation of said first field induced by thermal effects ofsaid exposing using the measurements; (b) determine correctiveinformation based on the assessed deformation; (c) correct the improvedexposure information based on said corrective information.
 9. Thearrangement of claim 8, wherein: a measurement station is connected tothe measurement port and arranged to. obtain measurement data regardingan exposed substrate comprising a pattern exposed using thepre-specified exposure information.
 10. The arrangement of any of claim7, wherein, in said model, predicting deformation at selected points isexpressed by:${{{dx}_{p} = {\sum\limits_{i}{T_{i}^{x}D_{i}^{x}}}};{and}}\mspace{14mu}$${{dy}_{p} = {\sum\limits_{i}{T_{i}^{y}D_{i}^{y}}}};{where}$ T_(i) ^(x)represents timing effects of exposing a target field C_(i) in anx-direction; T_(i) ^(y) represents timing effects of exposing a targetfield C_(i) in a y-direction; D_(i) ^(x) represents spatial effects inthe x-direction induced by a distance between a point within an exposedtarget field C_(i) and a point in a target field to be currentlyexposed; D_(i) ^(y) represents spatial effects in the y-directioninduced by a distance between a point within an exposed target fieldC_(i) and a point in a target field to be currently exposed; dx_(p):represents predicted deformation along the x axis; and dy_(p):represents predicted deformation along the y axis; and where$T_{i} = {{\exp( {- \frac{t - t_{i}}{\tau}} )}\mspace{14mu}{where}}$t represents absolute time; t_(i) represents time during which targetfield C_(i) is exposed; τ: represents a time sensitivity constant whichdepends on thermal properties of lithographic exposure components; and$D_{i} = {{k\mspace{14mu}{\exp( {- \frac{{r_{i} - r}}{\chi}} )}}:}$ represents effects induced by a distance |r_(i)−r| between an exposedfield and a field to be currently exposed in either the x or ydirection; r_(i) representing a point on target field C_(i); rrepresenting a point on the substrate W that is currently being exposed;χ representing spatial thermal properties of lithographic exposurecomponents; k: representing a proportionality constant that depends onthermal properties of lithographic exposure components.
 11. Thearrangement of claim 1, wherein said pre-specified exposure informationincludes one or more of the following: exposure energy information,exposure time information, exposure field position information, exposurefield sequencing information, and exposure field deformationinformation.
 12. The arrangement of claim 1, wherein the model isfurther based on an amount of energy transferred from the substrate to afirst material with which the substrate is in contact during a firstperiod.
 13. The arrangement of claim 12, wherein said amount of energyis modeled to be proportional to a logarithm of the period.
 14. Thearrangement of claim 12, wherein: the material is an immersion liquidand the thermally-induced field deformations are caused by cooling ofthe substrate due to evaporation of the immersion liquid.
 15. Thearrangement of claim 12, wherein, in said model, said predicting ofdeformation at the selected points based on a time-decayingcharacteristic is expressed by:${{dx}_{p} = {\sum\limits_{i}{T_{i}^{x}D_{i}^{x}}}};{and}$${{dy}_{p} = {\sum\limits_{i}{T_{i}^{y}D_{i}^{y}}}};{where}$ T_(i) ^(x)represents timing effects of exposing a target field C_(i) in anx-direction; T_(i) ^(y) represents timing effects of exposing a targetfield C_(i) in a y-direction; D_(i) ^(x) represents spatial effects inthe x-direction induced by a distance between a point within an exposedtarget field C_(i) and a point in a target field to be currentlyexposed; D_(i) ^(y) represents spatial effects in the y-directioninduced by a distance between a point within an exposed target fieldC_(i) and a point in a target field to be currently exposed; dx_(p):represents predicted deformation along the x axis; and dy_(p):represents predicted deformation along the y axis; and where$T_{i} = {{\exp( {- \frac{t - t_{i}}{\tau}} )}\mspace{14mu}{where}}$t represents absolute time; t_(i) represents time during which targetfield C_(i) is exposed; τ: represents a time sensitivity constant whichdepends on the thermal properties of lithographic exposure components;and${{D( {{\overset{\_}{r}}_{i},\overset{\_}{r}} )} = {{\sum\limits_{{i\text{:}{\overset{\_}{r}}_{j}} \in {{{SH}{(\overset{\_}{r})}}\bigcap W}}^{N}{( {{\overset{\_}{r}}_{j} - {\overset{\_}{r}}_{i}} ){{\exp( {{- {{{\overset{\_}{r}}_{j} - {\overset{\_}{r}}_{i}}}}/\chi} )}/{{{\overset{\_}{r}}_{j} - {\overset{\_}{r}}_{i}}}}}}:}}\mspace{14mu}$ represents effects induced by a distance |r_(i)−r|; SH( r):representing a combination of a final element of a projection system, areservoir provided with a seal member and arranged to be filled with theimmersion liquid, also referred to as “showerhead”; r_(i) representing apoint on target field C_(i) at which overlay is estimated; rrepresenting a point on the substrate that is currently being followedby the showerhead; and where χ: represents spatial thermal properties oflithographic exposure components; N is a maximal number needed forintegral estimation; and W is the substrate.